NAME______DATE______PER.______

SPRING FINAL EXAM:

4th 6-WEEKS REVIEW

PART 1. Solving Systems

Solve each system of equations, using your method of choice.

1) Solution: ______/ x – y = 6
2x + y = 0
2) Solution: ______/ q – 2r = 4
q + r = 37

Solve each problem as indicated.

3) Solution: ______/ Two lines have the given equations. At what point do they intersect?
2x – y = 1
3x = y – 6
4) x = ______/ If (x, -2) is a solution for the following system of equations, what is the value of x?
5x – y = 12
3x + y = 4

PART 2. System Applications

For each word problem, set up a system of equations, and solve for the value(s) indicated.

5) ______/ A rectangle has a perimeter of 18 cm. Its length is 5 cm more than its width. Find the dimensions.

6) ______/ Timmy has 180 marbles, some plain and some colored. If there are 32 more plain marbles than colored marbles, how many colored marbles does he have?

7) ______/ Jimmy had $5.25 in nickels and quarters. If he had 15 more nickels than quarters, how many coins of each type did he have?

8) ______/ Tickets for a school football game cost $1.00 each if purchased before the day of the game. They cost $1.50 each if bought at the gate. For the homecoming game, 600 tickets were sold, with receipts of $700. How many tickets were sold at the gate?

PART 3. Single Variable Inequalities

Solve each inequality and graph its solution set.

9) 6w + 4 ³ 5w + 4
Solution: ______/ 10) 4y + 2 < 8y – (6y – 10)
Solution: ______/ 11) 3(x + 2) £ 3x + 2
Solution: ______
12) -7 < 3x + 2 £ 14
Solution: ______/ 13) -2 < 2r – 4 < 6
Solution: ______

PART 4. Two-Variable Inequalities

Graph the inequality below.

14) 4x + y > 8

PART 5. Applications of Single Variable Inequalities.

For each problem set up an inequality and solve.

15) ______/ Mike sells used cars. He makes $250 per week plus $200 for each car he sells. Because of Mike’s cost of living, he needs to earn at least $1250 per week to pay off all of his extravagant bills. How many cars must he sell each week to accomplish this?
16) ______/
Crystal wants to have at least an 82 average in Algebra 1 this six weeks. She made a 75 and a 96 on the first two tests. What does she need to make on the third test to receive at least an 82 average?

PART 6. Systems of Inequalities

Graph the system of inequalities and shade the solution set heavily.

17) 2y + x < 6 3x – y > 4 /
18) Write the system of inequalities
represented by the graph shown.
System: ______
______/
19) The graph of the system of equations
x = 2
y = 2x + 3
is shown below. Would the point (1, 1)
be in the solution set of this system of
inequalities?
x £ 2
y £ 2x + 3
YES or NO /

PART 7. Adding & Subtracting Polynomials

Find each sum or difference.

20) ______/ (4x2 - 2x + 6) – (- x2 – 11x + 6) = _?_
21) ______/ ( x2 + 2x – 3) + (3x2 – 2x – 8) = _?_
22) ______/ What is the measure of the third side of a triangle if the P = 8x + 4y and two of the sides have measures of
x + 2y and 3x + y?

PART 8. Multiplying Monomials

Find each product.

23) ______/ ( 2x2y3 )(5x3) = _?_
24) ______/ (2x2)(3x6) – (4x4)(2x4) = _?_

PART 9. Powers of Monomials

25) ______/ (2ab2)2( -3a2b)2 = _?_
26) ______/ 9n3=

PART 10. Multiplying Polynomials

Find each product.

27) ______/
(x + 1)(2x – 3) = _?_
28) ______/ (a + b)(2a2 – ab + 3b2) = _?_

PART 11. Multiplying Monomials & Polynomials

Find each product.

29) ______/ –6a3(a2 – 2a + 1) = _?_
30) ______/ –2xy( x2 – 3xy + y2) = _?_

PART 12. Polynomials in Geometric Form

Answer each problem as indicated.

31) P = ______
A = ______/ Find the perimeter and area of the region below.

32) A = ______/ Find the area of the shaded region.

33) P = ______
A = ______/
Find the perimeter and the area of the rectangle:
34) P = ______
A = ______/ The length of the side of a square is 5x – 3. Find the perimeter and the area of the square.
35) V = ______/ Find the volume of the solid: